(Not applicable)
This invention relates generally to integrated inertial/GPS navigation systems and more specifically to integrated inertia/GPS navigation systems that achieve improved operational reliability through the use of a plurality of Kalman filters.
The Autonomous Integrity Monitored Extrapolation (AIME(trademark)) algorithm is an improved algorithm for integrating the Global Positioning System (GPS) with an inertial navigation system (INS) in a way that the navigation solution has a minimum susceptibility to equipment failures, interference, and jamming. The principal problem with using Kalman filters to integrate GPS with INS is that a slow GPS failure due to interference or spoofing can contaminate the integrated solution before it is detected. The AIME(trademark) algorithm solves this problem by analyzing the residuals of the filter over long time intervals before the corrections are added externally to the INS solution. Because the solution is based on the continuous INS output, it is extremely reliable, and continuous in case of complete loss of the GPS. By using parallel solutions which are not sensitive to the failure, it rejects the contamination and continues using an uncontaminated, reliable precision navigation solution.
This principle is applied in the present invention to carrier tracking. The basis of the invention is the Anti-Jam AIME(trademark) (AJ-AIME(trademark)) algorithm. This algorithm achieves at least 20 dB J/S improvement, and possibly 30-40 dB J/S improvement. This is in addition to the J/S improvements from other techniques. Previous solutions to improve J/S performance are based on deep coupling using a vector solution combining both carrier and code measurements and INS errors. These errors are estimated in a large, complex maximum likelihood estimator. One problem with these approaches is that the signals are no longer independent so that receiver autonomous integrity monitoring (RAIM) cannot be used to determine integrity.
The AJ-AIME(trademark) approach avoids the loss of integrity and possible contamination inherent in such vector approaches. Even if jamming is successful, the AIME(trademark) solution provides maximum accuracy for coasting with the calibrated INS solution, since this solution is uncontaminated from the period when jamming or interference first began.
For manned aircraft or long range missiles already equipped with a high-quality INS, the AIME(trademark) algorithm can be implemented in a separate, very inexpensive small box, which adds corrections to the INS solution. For inexpensive short range missiles, or munitions, without INS, the AIME(trademark) algorithm is combined with MEMS technology. This solution uses 1 deg/hr silicon gyros, 20 micro-g accelerometers, and a GPS receiver, all integrated in an inexpensive, small box.
Without WAAS, the failure detection and exclusion (FDE) availability of RAIM for non-precision approach (NPA) using 24-satellite constellations with up to three outages is less than 50%. Using WAAS for Precision Approach CAT I (DH=200 feet), the FDE availability of RAIM is less than 2%. One objective of this invention is to improve FDE availability by up to five orders of magnitude. RAIM is basically a xe2x80x9csnapshotxe2x80x9d approach using instantaneous noisy position data. Instead of RAIM, this invention uses an integrated systems approach. With today""s system technology, including micro-electro-mechanical system (MEMS) technology, and using Kalman filter algorithms, it is possible with this approach to use feedback from rate, acceleration, acceleration rate, etc., up to at least the fourth derivative of position, in the Kalman filter error model.
In order to reject errors caused by satellite clock failures, multipath, excessive atmospheric errors, or subsystem failures, these errors and all other errors are modeled in a bank of Kalman filters in the AIME(trademark) algorithm. Each of these filters is tuned for excessive errors in one channel, or in one group of channels, or in a subsystem. The filter which models the errors correctly will have uncorrelated residuals, because of the xe2x80x9cinnovations propertyxe2x80x9d of Kalman filters. By estimating the mean of the residuals over many Kalman filter cycles, a test statistic is obtained for each filter. This statistic is the mean-square estimated residual for that filter. The filter with the correct model will have the lowest test statistic and the output of that filter will be used. The other filters have large mean-square estimated residuals, since they do not correctly model the excessive error.
The word xe2x80x9cfailurexe2x80x9d is used herein to represent any excessive error which can contaminate the solution, whether due to an actual subsystem soft failure or due to a temporary excessive instrument error or signal error.
Recursive algorithms are used in order that the estimate can use very large numbers of Kalman filter cycles to detect slow failures. In present civil applications, these estimates use residuals over the past two hour period to detect and exclude errors due to slow satellite clock drifts. This algorithm has been certified for Primary Means and has been flown on commercial airliners for many years. In addition, many years of data have been collected and analyzed from flights in normal airline operation.
To improve anti-jam performance, other approaches have claimed that 30-40 dB J/S improvement can be achieved by a vector processing algorithm using deep coupling, where the INS is integrated with the measurements from both the carrier and code discriminators. This would be done in a large, complex, maximum-likelihood estimator which attempts to estimate all error sources including INS errors. This approach creates an integrity problem since the different satellite measurements are no longer independent, and RAIM-type integrity checking is no longer valid.
There are three additional difficulties with this approach: (1) it does not consider the fundamental problem that arises when integrating inertial information with carrier phase information, (2) it does not properly consider the unique characteristics of inertial system errors, and (3) it does not consider the very different characteristics of carrier phase errors vs. code errors.
The fundamental problem referred to in (1) above is that the wavelength of the carrier is only 19 centimeters. During turbulence or high dynamics, the separation between the INS and the GPS antenna makes it difficult to process changing inertial attitude information fast enough to aid the carrier tracking at the antenna to centimeter accuracy at 1000 Hz without excessive time lags.
The unique characteristics of inertial systems referred to in (2) above arise because inertial errors vary slowly. Gyro and accelerometer errors change at only a fraction of a micro-g per second. This causes phase errors of only a few micrometers per second. This is too small to estimate with short term phase measurements, which are noisy. It is much better to estimate these errors over long periods of time using PR measurements, which have bounded position errors over these long periods.
The difficulty identified in (3) above arises because pseudorange measurements are made at 1 Hz with an accuracy of meters while the carrier phase is measured at 1000 Hz with an accuracy of a centimeter or less. It is not practical to combine these measurements in the same Kalman filter. If they are combined, it is almost impossible to prevent contamination from individual signals.
The solution to (1) above (i.e. aiding the carrier discriminators in turbulence and dynamics) is to use strapdown measurements in body axes at 400 to 1600 Hz to compute the antenna position relative to the INS. These measurements are used to estimate antenna position a short time in the future at 1000 Hz. The short prediction time is adjusted to cancel time lags in the system. This effectively eliminates the dynamic stress that the carrier loop has to track.
The solution to (2) above (i.e. inertial characteristics) is to use only pseudorange information in a navigation Kalman filter with a large step size, such as 20 seconds or more, to estimate INS errors. These estimated corrections are added to the INS solution to obtain the 1000 Hz extrapolator aiding information for the carrier discriminators.
The solution to (3) above (i.e. carrier vs. code characteristics) is to use a separate AJ-AIME(trademark) Kalman filter for the carrier discriminator information. This Kalman filter has a much smaller update frequency of 1 Hz., to estimate slow corrections to the 1000-Hz phase discriminator data. The inertial extrapolator has already eliminated the dynamics from the measurements, and the navigation Kalman filter has eliminated slowly varying errors, such as user clock errors, atmospheric errors, and IMU instrument errors. The 1-Hz AJ-AIME(trademark) Kalman filter will only have to correct small, residual medium-frequency errors in the carrier tracking loop. This 1-Hz carrier loop filter will also use parallel banks of similar Kalman filters with residuals averaged over short and long periods to detect and reject phase error contamination.
Measurements for different satellites are no longer independent at the same update cycle, but this was never a requirement for AIME(trademark) integrity as it is for RAIM integrity. In fact, the AIME(trademark) residuals are highly correlated at each Kalman measurement cycle, but they are uncorrelated from one cycle to the next, provided there is no failure, and the model is correct.
In military applications, the AIME(trademark) navigation Kalman filter cycle time can be reduced from 60 seconds, as used in civil applications, to 20 seconds. This navigation Kalman filter is then used to aid a second ANTI-JAM AIME(trademark) (AJ-AIME(trademark)) Kalman filter with cycle time of only one second. This filter in turn aids an inertial extrapolator, operating at 1000 Hz., which is used to eliminate the high frequency dynamics from the carrier tracking loop. This provides J/S improvement of 30-40 dB. The objective is to reject multipath, unintentional anomalies or interference, jamming, and spoofing, and to continue carrier tracking for more than a minute with complete loss of the GPS signal, as caused by masking due to aircraft or missile motion.
Definitions of symbols used herein are as follows.
Ax, Ay, Az, Non-gravitational accelerations along navigation axes
ADIRS Air Data Inertial Reference System
AHRS Attitude and heading reference system
AIME(trademark) Autonomous integrity monitored extrapolation
AJ-AIME(trademark) Anti-Jam autonomous integrity monitored extrapolation
[CRB] Direction cosine matrix from Body to navigation Reference axes
CAT I Category of precision approach with 200 foot decision height
DGPS Differential Global Positioning System
DH Decision height for approach to landing
FDE Failure detection and exclusion
FOM Figure of Merit
HDOP Horizontal Dilution of Precision
HIL Horizontal integrity level
HPL Horizontal protection level
IMU Inertial measurement unit
INS Inertial navigation system
IRS Inertial reference system
J/S Ratio of jamming power to signal power, usually measured in dB
MEMS Micro-electro-mechanical system
NPA Non precision approach
OCS Operational Control Segment
PR Pseudo Range measurement from GPS
R Earth radius
RLB Lever arm from IMU to GPS antenna in body axes
RAIM Receiver autonomous integrity monitoring
SA Selective Availability
VDLL Vector delay lock loop
VPL Vertical protection level
WAAS Wide Area Augmentation System
deg/hr angular rate unit of degrees per hour
g unit of acceleration equal to 32.2 feet/second2 
{overscore (xcfx89)} Total spatial angular rate of navigation coordinates (earth rate+craft rate)
xcfx84 Correlation time of first order Markov process
Definitions of Kalman filter symbols used herein are as follows.
KF Kalman filter
k Index of Kalman filter cycle, or navigation solution cycle
M,N Dimension of measurement vector, error state vector, resp.
rk Residual vector of Kalman filter, dimension (Mxc3x971)
Vk Covariance matrix of residuals, dimension (Mxc3x97M)
rest Estimated mean residual vector of Kalman filter, dimension (Mxc3x971)
Vest Covariance matrix of estimated mean residual vector, dimension (Mxc3x97M)
sest2 Test statistic
zk Measurement vector of Kalman filter
Hk, F Observation matrix (Mxc3x97N), dynamics matrix Nxc3x97N), resp.
xkxe2x88x92, xk+ Error state vector before, and after, update, resp., dimension (Nxc3x971)
Rk, Qk Measurement noise (Mxc3x97M), Process noise Nxc3x97N), resp.
Pkxe2x88x92, Pk+ Error state Covariance matrix before, and after update, dimension (Nxc3x97N)
Kk Kalman gain matrix, dimension (Nxc3x97M)
T Superscript indicating transpose of matrix
xe2x88x921 Superscript indicating inverse of matrix
zi(t) Measurement from ith satellite at time t
xz(t) Temporary error state used to make measurement at time t
PRic(xz(t)) Pseudorange computed from error state xz(t)
PRim(t) Pseudorange measured at time t
"PHgr"(txe2x88x92tk) Transition matrix from time tk to time t
excfx86ic(xz(t)) Computed phase errors at time t
excfx86im(t) Measured phase errors at time t
The invention is a method and apparatus for adjusting the phase and frequency of a received GPS signal in an inertial-GPS navigation system comprising an inertial measurement unit (IMU) and a GPS receiver where the GPS receiver is postulated as having an input port for inputting a delta-phase at delta-time intervals into a received satellite signal and an output port for outputting a carrier phase error defined as the difference between the actual phase of the received GPS signal and a reference value. The GPS receiver is also postulated as having an output port for outputting a pseudorange associated with the received GPS signal. The IMU is postulated as having an output port for outputting the acceleration and angular velocity of the IMU.
The method comprises the steps of determining two delta-phase components: (a) a Kalman delta-phase component and (b) an IMU delta-phase component. The Kalman delta-phase component is derived from a plurality of candidate Kalman delta-phase components obtained by performing a first set of more than one Kalman filter processes. The inputs to each first-set Kalman filter process include the carrier phase error and a position vector associated with the IMU. A candidate Kalman delta-phase component is produced as an output of each first-set Kalman filter process. The Kalman delta-phase component is determined from a candidate Kalman delta-phase components selected from the plurality of candidate Kalman delta-phase components by applying a predetermined Kalman delta-phase component selection rule.
The IMU delta-phase component is derived from the IMU outputs and a direction-cosine matrix that translates the body coordinates of the IMU into the navigation coordinates of the inertial-GPS navigation system.